Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the word setting:
“We believe that Carlyle has, after all, more readers, and is better known to-day for this very originality of style, and that posterity will have reason to thank him for emancipating the language, in some measure, from the fetters which a merely conservative, aimless, and pedantic literary class had imposed upon it, and setting an example of greater freedom and naturalness.”
—Henry David Thoreau (1817–1862)
“Like plowing, housework makes the ground ready for the germination of family life. The kids will not invite a teacher home if beer cans litter the living room. The family isn’t likely to have breakfast together if somebody didn’t remember to buy eggs, milk, or muffins. Housework maintains an orderly setting in which family life can flourish.”
—Letty Cottin Pogrebin (20th century)
“When I consider the clouds stretched in stupendous masses across the sky, frowning with darkness or glowing with downy light, or gilded with the rays of the setting sun, like the battlements of a city in the heavens, their grandeur appears thrown away on the meanness of my employment; the drapery is altogether too rich for such poor acting. I am hardly worthy to be a suburban dweller outside those walls.”
—Henry David Thoreau (1817–1862)